Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2, 3, 4, 5, 6, 7, 8, 9, 10*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
2	reference	73	⊢
3	reference	51	⊢
4	reference	34	⊢
5	reference	19	⊢
6	reference	35	⊢
7	reference	40	⊢
8	reference	21	⊢
9	reference	22	⊢
10	instantiation	23, 11, 12	⊢
	: , : , :
11	instantiation	13, 51, 14, 15, 16, 17	⊢
	: , : , : , :
12	instantiation	18, 73, 51, 34, 19, 35, 20, 21, 22	⊢
	: , : , : , : , : , :
13	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
14	instantiation	41	⊢
	: , :
15	instantiation	41	⊢
	: , :
16	instantiation	23, 24, 25	⊢
	: , : , :
17	instantiation	26, 40	⊢
	:
18	theorem		⊢
	proveit.numbers.addition.disassociation
19	instantiation	41	⊢
	: , :
20	instantiation	27, 28, 29	⊢
	: , : , :
21	instantiation	71, 43, 47	⊢
	: , : , :
22	instantiation	71, 43, 65	⊢
	: , : , :
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	33, 73, 51, 34, 30, 35, 40, 39, 37	⊢
	: , : , : , : , : , :
25	instantiation	31, 34, 73, 35, 40, 39, 37	⊢
	: , : , : , : , : , : , :
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
27	theorem		⊢
	proveit.logic.equality.sub_right_side_into
28	instantiation	38, 32, 37	⊢
	: , :
29	instantiation	33, 34, 51, 73, 35, 36, 39, 40, 37	⊢
	: , : , : , : , : , :
30	instantiation	41	⊢
	: , :
31	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
32	instantiation	38, 39, 40	⊢
	: , :
33	theorem		⊢
	proveit.numbers.multiplication.disassociation
34	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
35	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36	instantiation	41	⊢
	: , :
37	instantiation	71, 43, 58	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
39	instantiation	71, 43, 42	⊢
	: , : , :
40	instantiation	71, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
42	instantiation	71, 67, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	46, 47, 65	⊢
	: , :
45	instantiation	71, 69, 48	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
47	instantiation	71, 49, 50	⊢
	: , : , :
48	instantiation	71, 72, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
50	instantiation	52, 53, 54	⊢
	: , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
52	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
53	instantiation	71, 55, 56	⊢
	: , : , :
54	instantiation	57, 58, 59	⊢
	:
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
56	instantiation	71, 60, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
58	instantiation	62, 64, 65, 66	⊢
	: , : , :
59	instantiation	63, 64, 65, 66	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
61	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
65	instantiation	71, 67, 68	⊢
	: , : , :
66	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
68	instantiation	71, 69, 70	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
70	instantiation	71, 72, 73	⊢
	: , : , :
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements